| ckw03_c |
|
Table of contents
Procedure
ckw03_c ( C-Kernel, write segment to C-kernel, data type 3 )
void ckw03_c ( SpiceInt handle,
SpiceDouble begtim,
SpiceDouble endtim,
SpiceInt inst,
ConstSpiceChar * ref,
SpiceBoolean avflag,
ConstSpiceChar * segid,
SpiceInt nrec,
ConstSpiceDouble sclkdp [],
ConstSpiceDouble quats [][4],
ConstSpiceDouble avvs [][3],
SpiceInt nints,
ConstSpiceDouble starts [] )
AbstractAdd a type 3 segment to a C-kernel. Required_ReadingCK DAF SCLK KeywordsPOINTING UTILITY Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- handle I Handle of an open CK file. begtim I The beginning encoded SCLK of the segment. endtim I The ending encoded SCLK of the segment. inst I The NAIF instrument ID code. ref I The reference frame of the segment. avflag I SPICETRUE if the segment will contain angular velocity. segid I Segment identifier. nrec I Number of pointing records. sclkdp I Encoded SCLK times. quats I Quaternions representing instrument pointing. avvs I Angular velocity vectors. nints I Number of intervals. starts I Encoded SCLK interval start times. Detailed_Input
handle is the handle of the CK file to which the segment will
be written. The file must have been opened with write
access.
begtim is the beginning encoded SCLK time of the segment. This
value should be less than or equal to the first time in
the segment.
endtim is the encoded SCLK time at which the segment ends.
This value should be greater than or equal to the last
time in the segment.
inst is the NAIF integer ID code for the instrument.
ref is a character string which specifies the
reference frame of the segment. This should be one of
the frames supported by the SPICELIB routine NAMFRM
which is an entry point of FRAMEX.
The rotation matrices represented by the quaternions
that are to be written to the segment transform the
components of vectors from the inertial reference frame
specified by ref to components in the instrument fixed
frame. Also, the components of the angular velocity
vectors to be written to the segment should be given
with respect to ref.
ref should be the name of one of the frames supported
by the SPICELIB routine NAMFRM.
avflag is a boolean flag which indicates whether or not the
segment will contain angular velocity.
segid is the segment identifier. A CK segment identifier may
contain up to 40 characters, excluding the terminating
null.
nrec is the number of pointing instances in the segment.
sclkdp are the encoded spacecraft clock times associated with
each pointing instance. These times must be strictly
increasing.
quats is an array of SPICE-style quaternions representing a
sequence of C-matrices. See the discussion of "Quaternion
Styles" in the -Particulars section below.
The C-matrix represented by the ith quaternion in
quats is a rotation matrix that transforms the
components of a vector expressed in the inertial
frame specified by ref to components expressed in
the instrument fixed frame at the time sclkdp[i].
Thus, if a vector V has components x, y, z in the
inertial frame, then V has components x', y', z' in
the instrument fixed frame where:
[ x' ] [ ] [ x ]
| y' | = | cmat | | y |
[ z' ] [ ] [ z ]
avvs are the angular velocity vectors ( optional ).
The ith vector in avvs gives the angular velocity of
the instrument fixed frame at time sclkdp[i]. The
components of the angular velocity vectors should
be given with respect to the inertial reference frame
specified by ref.
The direction of an angular velocity vector gives
the right-handed axis about which the instrument fixed
reference frame is rotating. The magnitude of the
vector is the magnitude of the instantaneous velocity
of the rotation, in radians per second.
If avflag is SPICEFALSE then this array is ignored by the
routine; however it still must be supplied as part of
the calling sequence.
nints is the number of intervals that the pointing instances
are partitioned into.
starts are the start times of each of the interpolation
intervals. These times must be strictly increasing
and must coincide with times for which the segment
contains pointing.
Detailed_OutputNone. See -Files section. ParametersNone. Exceptions
1) If `handle' is not the handle of a C-kernel opened for writing,
an error is signaled by a routine in the call tree of this
routine.
2) If `segid' is more than 40 characters long, the error
SPICE(SEGIDTOOLONG) is signaled by a routine in the call tree
of this routine.
3) If `segid' contains any non-printable characters, the error
SPICE(NONPRINTABLECHARS) is signaled by a routine in the call
tree of this routine.
4) If the first encoded SCLK time is negative, the error
SPICE(INVALIDSCLKTIME) is signaled by a routine in the call
tree of this routine.
5) If the second encoded SCLK or any subsequent times, or if the
encoded SCLK times are not strictly increasing, the error
SPICE(TIMESOUTOFORDER) is signaled by a routine in the call
tree of this routine.
6) If `begtim' is greater than sclkdp[0] or `endtim' is less than
sclkdp[nrec-1], the error SPICE(INVALIDDESCRTIME) is signaled by
a routine in the call tree of this routine.
7) If the name of the reference frame is not one of those
supported by the CSPICE routine namfrm_c, the error
SPICE(INVALIDREFFRAME) is signaled by a routine in the call
tree of this routine.
8) If `nrec', the number of pointing records, is less than or equal
to 0, the error SPICE(INVALIDNUMREC) is signaled by a routine
in the call tree of this routine.
9) If `nints', the number of interpolation intervals, is less than
or equal to 0, the error SPICE(INVALIDNUMINT) is signaled by a
routine in the call tree of this routine.
10) If the encoded SCLK interval start times are not strictly
increasing, the error SPICE(TIMESOUTOFORDER) is signaled by a
routine in the call tree of this routine.
11) If an interval start time does not coincide with a time for
which there is an actual pointing instance in the segment, the
error SPICE(INVALIDSTARTTIME) is signaled by a routine in the
call tree of this routine.
12) This routine assumes that the rotation between adjacent
quaternions that are stored in the same interval has a
rotation angle of `theta' radians, where
0 <= theta < pi.
The routines that evaluate the data in the segment produced
by this routine cannot distinguish between rotations of `theta'
radians, where `theta' is in the interval [0, pi), and
rotations of
theta + 2 * k * pi
radians, where k is any integer. These `large' rotations
will yield invalid results when interpolated. You must
ensure that the data stored in the segment will not be
subject to this sort of ambiguity.
13) If any quaternion has magnitude zero, the error
SPICE(ZEROQUATERNION) is signaled by a routine in the call
tree of this routine.
14) If the start time of the first interval and the time of the
first pointing instance are not the same, the error
SPICE(TIMESDONTMATCH) is signaled by a routine in the call
tree of this routine.
15) If any of the `ref' or `segid' input string pointers is null,
the error SPICE(NULLPOINTER) is signaled.
16) If any of the `ref' or `segid' input strings has zero length,
the error SPICE(EMPTYSTRING) is signaled.
FilesThis routine adds a type 3 segment to a C-kernel. The C-kernel may be either a new one or an existing one opened for writing. Particulars
For a detailed description of a type 3 CK segment please see the
CK Required Reading.
This routine relieves the user from performing the repetitive
calls to the DAF routines necessary to construct a CK segment.
Quaternion Styles
-----------------
There are different "styles" of quaternions used in
science and engineering applications. Quaternion styles
are characterized by
- The order of quaternion elements
- The quaternion multiplication formula
- The convention for associating quaternions
with rotation matrices
Two of the commonly used styles are
- "SPICE"
> Invented by Sir William Rowan Hamilton
> Frequently used in mathematics and physics textbooks
- "Engineering"
> Widely used in aerospace engineering applications
CSPICE function interfaces ALWAYS use SPICE quaternions.
Quaternions of any other style must be converted to SPICE
quaternions before they are passed to CSPICE functions.
Relationship between SPICE and Engineering Quaternions
------------------------------------------------------
Let M be a rotation matrix such that for any vector V,
M*V
is the result of rotating V by theta radians in the
counterclockwise direction about unit rotation axis vector A.
Then the SPICE quaternions representing M are
(+/-) ( cos(theta/2),
sin(theta/2) A(1),
sin(theta/2) A(2),
sin(theta/2) A(3) )
while the engineering quaternions representing M are
(+/-) ( -sin(theta/2) A(1),
-sin(theta/2) A(2),
-sin(theta/2) A(3),
cos(theta/2) )
For both styles of quaternions, if a quaternion q represents
a rotation matrix M, then -q represents M as well.
Given an engineering quaternion
QENG = ( q0, q1, q2, q3 )
the equivalent SPICE quaternion is
QSPICE = ( q3, -q0, -q1, -q2 )
Associating SPICE Quaternions with Rotation Matrices
----------------------------------------------------
Let FROM and TO be two right-handed reference frames, for
example, an inertial frame and a spacecraft-fixed frame. Let the
symbols
V , V
FROM TO
denote, respectively, an arbitrary vector expressed relative to
the FROM and TO frames. Let M denote the transformation matrix
that transforms vectors from frame FROM to frame TO; then
V = M * V
TO FROM
where the expression on the right hand side represents left
multiplication of the vector by the matrix.
Then if the unit-length SPICE quaternion q represents M, where
q = (q0, q1, q2, q3)
the elements of M are derived from the elements of q as follows:
.- -.
| 2 2 |
| 1 - 2*( q2 + q3 ) 2*(q1*q2 - q0*q3) 2*(q1*q3 + q0*q2) |
| |
| |
| 2 2 |
M = | 2*(q1*q2 + q0*q3) 1 - 2*( q1 + q3 ) 2*(q2*q3 - q0*q1) |
| |
| |
| 2 2 |
| 2*(q1*q3 - q0*q2) 2*(q2*q3 + q0*q1) 1 - 2*( q1 + q2 ) |
| |
`- -.
Note that substituting the elements of -q for those of q in the
right hand side leaves each element of M unchanged; this shows
that if a quaternion q represents a matrix M, then so does the
quaternion -q.
To map the rotation matrix M to a unit quaternion, we start by
decomposing the rotation matrix as a sum of symmetric
and skew-symmetric parts:
2
M = [ I + (1-cos(theta)) OMEGA ] + [ sin(theta) OMEGA ]
symmetric skew-symmetric
OMEGA is a skew-symmetric matrix of the form
.- -.
| 0 -n3 n2 |
| |
OMEGA = | n3 0 -n1 |
| |
| -n2 n1 0 |
`- -'
The vector N of matrix entries (n1, n2, n3) is the rotation axis
of M and theta is M's rotation angle. Note that N and theta
are not unique.
Let
C = cos(theta/2)
S = sin(theta/2)
Then the unit quaternions Q corresponding to M are
Q = +/- ( C, S*n1, S*n2, S*n3 )
The mappings between quaternions and the corresponding rotations
are carried out by the CSPICE routines
q2m_c {quaternion to matrix}
m2q_c {matrix to quaternion}
m2q_c always returns a quaternion with scalar part greater than
or equal to zero.
SPICE Quaternion Multiplication Formula
---------------------------------------
Given a SPICE quaternion
Q = ( q0, q1, q2, q3 )
corresponding to rotation axis A and angle theta as above, we can
represent Q using "scalar + vector" notation as follows:
s = q0 = cos(theta/2)
v = ( q1, q2, q3 ) = sin(theta/2) * A
Q = s + v
Let Q1 and Q2 be SPICE quaternions with respective scalar
and vector parts s1, s2 and v1, v2:
Q1 = s1 + v1
Q2 = s2 + v2
We represent the dot product of v1 and v2 by
<v1, v2>
and the cross product of v1 and v2 by
v1 x v2
Then the SPICE quaternion product is
Q1*Q2 = s1*s2 - <v1,v2> + s1*v2 + s2*v1 + (v1 x v2)
If Q1 and Q2 represent the rotation matrices M1 and M2
respectively, then the quaternion product
Q1*Q2
represents the matrix product
M1*M2
Examples
The numerical results shown for this example may differ across
platforms. The results depend on the SPICE kernels used as
input, the compiler and supporting libraries, and the machine
specific arithmetic implementation.
1) Create a CK type 3 segment; fill with data for a simple time
dependent rotation and angular velocity.
Example code begins here.
/.
Program ckw03_ex1
./
#include "SpiceUsr.h"
int main( )
{
/.
Local parameters.
./
#define CK3 "ckw03_ex1.bc"
#define SPTICK 0.001
#define INST -77703
#define MAXREC 201
/.
Local variables.
./
SpiceChar * ref;
SpiceChar * ifname;
SpiceChar * segid;
SpiceDouble avvs [MAXREC][3];
SpiceDouble begtim;
SpiceDouble endtim;
SpiceDouble quats [MAXREC][4];
SpiceDouble rate;
SpiceDouble rwmat [3][3];
SpiceDouble spaces;
SpiceDouble sclkdp [MAXREC];
SpiceDouble starts [MAXREC/2];
SpiceDouble sticks;
SpiceDouble theta;
SpiceDouble wmat [3][3];
SpiceDouble wquat [4];
SpiceInt handle;
SpiceInt i;
SpiceInt ncomch;
SpiceInt nints;
SpiceBoolean avflag;
/.
`ncomch' is the number of characters to reserve for the
kernel's comment area. This example doesn't write
comments, so set to zero.
./
ncomch = 0;
/.
The base reference from for the rotation data.
./
ref = "J2000";
/.
Time spacing in encoded ticks and in seconds
./
sticks = 10.0;
spaces = sticks * SPTICK;
/.
Declare an angular rate in radians per sec.
./
rate = 1.e-2;
/.
Internal file name and segment ID.
./
segid = "Test type 3 CK segment";
ifname = "Test CK type 3 segment created by ckw03_c";
/.
Open a new kernel.
./
ckopn_c ( CK3, ifname, ncomch, &handle );
/.
Create a 3x3 double precision identity matrix.
./
ident_c ( wmat );
/.
Convert the matrix to quaternion.
./
m2q_c ( wmat, wquat );
/.
Copy the work quaternion to the first row of
`quats'.
./
moved_c ( wquat, 4, quats[0] );
/.
Create an angular velocity vector. This vector is in the
`ref' reference frame and indicates a constant rotation
about the Z axis.
./
vpack_c ( 0.0, 0.0, rate, avvs[0] );
/.
Set the initial value of the encoded ticks.
./
sclkdp[0] = 1000.0;
/.
Fill the rest of the `avvs' and `quats' matrices
with simple data.
./
for ( i = 1; i < MAXREC; i++ )
{
/.
Create the corresponding encoded tick value in
increments of `sticks' with an initial value of
1000.0 ticks.
./
sclkdp[i] = 1000.0 + i * sticks;
/.
Create the transformation matrix for a rotation of
`theta' about the Z axis. Calculate `theta' from the
constant angular rate `rate' at increments of `spaces'.
./
theta = i * rate * spaces;
rotmat_c ( wmat, theta, 3, rwmat );
/.
Convert the `rwmat' matrix to SPICE type quaternion.
./
m2q_c ( rwmat, wquat );
/.
Store the quaternion in the `quats' matrix.
Store angular velocity in `avvs'.
./
moved_c ( wquat, 4, quats[i] );
vpack_c ( 0.0, 0.0, rate, avvs[i] );
}
/.
Create an array start times for the interpolation
intervals. The end time for a particular interval is
determined as the time of the final data value prior in
time to the next start time.
./
nints = MAXREC/2;
for ( i = 0; i < nints; i++ )
{
starts[i] = sclkdp[i*2];
}
/.
Set the segment boundaries equal to the first and last
time for the data arrays.
./
begtim = sclkdp[0];
endtim = sclkdp[MAXREC-1];
/.
This segment contains angular velocity.
./
avflag = SPICETRUE;
/.
All information ready to write. Write to a CK type 3
segment to the file indicated by `handle'.
./
ckw03_c ( handle, begtim, endtim, INST, ref, avflag, segid,
MAXREC, sclkdp, quats, avvs, nints, starts );
/.
SAFELY close the file.
./
ckcls_c ( handle );
return ( 0 );
}
When this program is executed, no output is presented on
screen. After run completion, a new CK file exists in the
output directory.
Restrictions
1) The creator of the segment is given the responsibility for
determining whether it is reasonable to interpolate between
two given pointing values.
2) This routine assumes that the rotation between adjacent
quaternions that are stored in the same interval has a
rotation angle of THETA radians, where
0 <= THETA < pi.
The routines that evaluate the data in the segment produced
by this routine cannot distinguish between rotations of THETA
radians, where THETA is in the interval [0, pi), and
rotations of
THETA + 2 * k * pi
radians, where k is any integer. These "large" rotations will
yield invalid results when interpolated. You must ensure that
the data stored in the segment will not be subject to this
sort of ambiguity.
3) All pointing instances in the segment must belong to one and
only one of the intervals.
Literature_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) B.V. Semenov (JPL) E.D. Wright (JPL) Version
-CSPICE Version 2.0.1, 10-AUG-2021 (JDR)
Edited the header to comply with NAIF standard. Created
complete code example from existing fragment.
-CSPICE Version 2.0.0, 01-JUN-2010 (NJB)
The check for non-unit quaternions has been replaced
with a check for zero-length quaternions. (The
implementation of the check is located in ckw03_.)
-CSPICE Version 1.4.2, 27-FEB-2008 (NJB)
Updated header; added information about SPICE
quaternion conventions.
-CSPICE Version 1.4.1, 27-SEP-2005 (BVS)
Added an item for SPICE(TIMESDONTMATCH) exception to the
-Exceptions section of the header.
-CSPICE Version 1.3.1, 07-JAN-2004 (EDW)
Trivial typo correction in index entries section.
-CSPICE Version 1.3.0, 28-AUG-2001 (NJB)
Changed prototype: inputs sclkdp, quats, avvs, and starts
are now const-qualified. Implemented interface macros for
casting these inputs to const.
-CSPICE Version 1.2.0, 02-SEP-1999 (NJB)
Local type logical variable now used for angular velocity
flag used in interface of ckw03_.
-CSPICE Version 1.1.0, 08-FEB-1998 (NJB)
References to C2F_CreateStr_Sig were removed; code was
cleaned up accordingly. String checks are now done using
the macro CHKFSTR.
-CSPICE Version 1.0.0, 25-OCT-1997 (NJB)
Based on SPICELIB Version 2.0.0, 28-DEC-1993 (WLT)
Index_Entrieswrite CK type_3 pointing data segment |
Fri Dec 31 18:41:02 2021